Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging

• URL: http://arxiv.org/abs/2602.07466v2
• Date: Fri, 13 Feb 2026 08:22:16 GMT
• Title: Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging
• Authors: Manuel Haas, Thomas Grandits, Thomas Pinetz, Thomas Beiert, Simone Pezzuto, Alexander Effland,
• Abstract summary: We introduce a space-time regularization framework that couples temporal regularization with a learned Fields-of-Experts (FoE)<n>We derive a finite discrere element on cardiac surface meshes, prove Mosco-convergence, and develop a scalable optimization algorithm capable of handling the FoE term.
• Score: 33.8053325455413
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Electrocardiographic imaging (ECGI) seeks to reconstruct cardiac electrical activity from body-surface potentials noninvasively. However, the associated inverse problem is severely ill-posed and requires robust regularization. While classical approaches primarily employ spatial smoothing, the temporal structure of cardiac dynamics remains underexploited despite its physiological relevance. We introduce a space-time regularization framework that couples spatial regularization with a learned temporal Fields-of-Experts (FoE) prior to capture complex spatiotemporal activation patterns. We derive a finite element discretization on unstructured cardiac surface meshes, prove Mosco-convergence, and develop a scalable optimization algorithm capable of handling the FoE term. Numerical experiments on synthetic epicardial data demonstrate improved denoising and inverse reconstructions compared to handcrafted spatiotemporal methods, yielding solutions that are both robust to noise and physiologically plausible.

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